Short Answer 
To calculate activation energy using the Arrhenius equation, first understand the logarithmic form: log (k2/k1) = Ea / 2.303R (1/T1 – 1/T2). By substituting the provided values and solving, the activation energy is found to be approximately 184,000 J/mol (184 kJ/mol).
Step 1: Understand the Arrhenius Equation
The first step in calculating the activation energy is to understand the Arrhenius equation, which relates the rate constants of a reaction at two different temperatures. The logarithmic form of the Arrhenius equation is:
- log (k2/k1) = Ea / 2.303R (1/T1 – 1/T2)
Here, k1 and k2 are the rate constants at temperatures T1 and T2, respectively, and Ea is the activation energy. We need to gather the values for rate change, temperatures, and the ideal gas constant.
Step 2: Substitute the Values
Next, substitute the known values into the Arrhenius equation. For this problem, the following values are provided:
- Rate change (k2/k1) = 3 (meaning the rate triples)
- T1 = 17°C = 290K
- T2 = 27°C = 300K
- 2.303R = 19.15 J/K mol
Plugging these values into the equation allows us to isolate and solve for Ea. Calculate the temperature term (1/T1 – 1/T2) to facilitate the calculation.
Step 3: Calculate Activation Energy
The final step is to simplify and solve the equation to find the activation energy (Ea). After inserting the calculated values back into the equation:
- Calculate: log 3 ‚Äöaa 0.48
- Solve for Ee using your results: 21.155256 / 0.000115
Upon solving, the result will yield an activation energy of approximately 184,000 J/mol, or 184 kJ/mol, indicating the energy required to start this reaction.